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Evaluate \int \frac{3 x^{2}}{x^{6}+1} d x
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Evaluate \int \frac{3 x^{2}}{x^{6}+1} d x

\int \frac{3 \mathrm{x}^{2} \mathrm{dx}}{\mathrm{x}^{6}+1}
=\int \frac{3 \mathrm{x}^{2} \mathrm{dx}}{\left(\mathrm{x}^{3}\right)^{2}+1}
\mathrm{t}=\mathrm{x}^{3} \Rightarrow \mathrm{dt}=3 \mathrm{x}^{2} \mathrm{dx}
=\int \frac{\mathrm{dt}}{\mathrm{t}^{2}+1}
=\tan ^{-1} \mathrm{t}+\mathrm{c} where \mathrm{c} is the constant of integration.
=\tan ^{-1}\left(\mathrm{x}^{3}\right)+\mathrm{c} where \mathrm{t}=\mathrm{x}^{3}

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